Yes, it should all be in that one file.

I think it should work the way you are doing it, but you may want to try this:

1. Install 2019 on the new computer (including the State).
2. Put the 2019 client files in the 2019 Data folder.
3. Open the 2019 program, verify the State information is there.
4. Then transfer 2019 to 2020.

However, there are other files that you may find useful, especially the "common" folder files.  So you may want to transfer the "common" file, or even the entire ProSeries folder to the new computer.  You can do that with both 2019 and 2020.  In the event you don't have 2020 installed on the old computer, you may consider installing 2020, then transfer all of the folders/files to the new computer (especially the "common" folder).